Determination of activity of 51 Cr source on gamma radiation measurements V.V.Gorbachev, V.N.Gavrin, T.V.Ibragimova, A.V.Kalikhov, Yu.M.Malyshkin,A.A.Shikhin Institute for Nuclear Research, RAS 1 The Intrnational workshop on Prospects of Particle Physics: Neutrino Physycs and Astrophysics Valday, Russia, Feb BNO INR RAS

Neutrino experiments of new generation on search of thin effects, accuracy <5% Experiments with artificial sources of a neutrino Transitions to sterile states Magnetic moment, … Experiment BEST (The Baksan experiment on sterile transitions) Radiation of the Ga target (50 t) of the solar neutrino detector of SAGE Neutrino source 51 Cr, 3 МCi Total systematic uncertainty ~2.6% The expected error of measurement of activity of the source <1 % How to measure the activity of 51 Cr: 1) On thermal emission – calorimetric method (36.7 keV/decay) 2) On gamma radiation 2

BEST: 2-zone gallium experiment on search for short baseline oscillations (Δm 2 ~ 1 eV 2 ) Target – 50 t of metallic Ga Masses of target in zones: 8 t and 42 t Path length in each zone =55 cm 51 Cr source: T 1/2 =27.7 d, 3 MCi E ν = 750 keV (90%), > 95 % captures 430 keV (10%) measurements on two bases experiment on nuclear capture 71 Ga+ν e → 71 Ge + e – Evidence for oscillations: 1) different capture rates in zones of target 2) suppression of capture rates in both zones

4 Gamma radiation 51 Сr keV, 10% decays 2.IB, <430 keV, 1.2·10 -4 x IB, <750 keV, 3.8·10 -4 x Internal Bremsstrahlung: Radiation spectrum in the source Activity is distributed unevenly on volume Radiation spectrum beyond the shield

5 The method of measurement We divide (mentally) the source on N parts (for example, with uniform activity): Source: Cr, 7.2 g/cm 3, cylinder ø8.6 x 9.5 cm Shield: W alloy, 16.6 g/сm 3, thickness 2.5 сm In the detector we register a signal – the sum of signals from all parts : Details are in the paper of V. Gorbachev, Yu.M.Malyshkin, to be published in Instruments and Experimental Techniques,(2015)

6 Signal in detector : и Here В i – absolute activity of i-th part and it does not depend on Е; f(E) – release of photon with energy Е per 1 decay And total activity: Then signal is: or entering replacement А(Е,x i ) – activity of i-th part of the source on photons with energy Е x i – i-th part of the source coordinate ε(E,x i ) – efficiency of detection of photons with energy Е from part x i

or in matrix form: One forms a system of linear equations for N j energy intervals {Е j } : In case N j =N, the solution will be : Condition for solution: It is convenient to solve the system of equations using method χ 2 : 1) more information is used (N j can be more than N) 2) the errors are estimated directly For uncorrelated errors: The errors σ(B i ) are determined on the boundaries of areas: 7

Calculation of the Compton scattering Spectrum of photons, which leave the shielding of the source, is distorted: monochromatic photons with energy Е have continuous spectrum with energies Е’ ≤ Е Δ j – signal from photons, registered in the energy range E j, but emitted with energy E > E j : Result: где ε ijj’ – exit from the i-th part of the source of photons with energy E j, generated with energy E j’ > E j I.e. the notation of the signal does not change and all described operations (solutions) remain the same after the change ε ij ’ to ε ij ’’ 8

N parts of the source requires N j ≥ N energy ranges In case the source is separated in 3 parts in each coordinate, N=3 3 =27 I.e, it is necessary to separate the spectrum of 51 Cr from 300 to 750 keV in N~27 ranges The width of one range Δ ~ ( )/27 = 15 keV Detector resolution~ 15 keV/ 750 keV= 2% I.e. one can use the Ge SCD On detector resolution 9

Why we need the collimator: 1) To limit the regions with equal efficiency in the detector 2) To remove the reflected (from the walls) radiation 3) To separate the registration efficiency on directions, to fit the condition 10 Uniformity of efficiency: simulations for ø=1cm and ø 2 cm Collimator

Expected counting rate From Monte Carlo (Geant4) Exit beyond the limits of the primary shielding: 320 keV – 2.8·10 -6 IB 430 keV – 1.5·10 -6 IB 750 keV – 5.1·10 -4 The total number of photons outside the shielding will be 5.1·10 10 s -1 per decay Of them 320 keV – 61%, IB 750 keV – 39%, IB 430 keV– 4·10 -3 % At a distance of 10 m with collimator 1 сm one can expect 3000 photons/sec 11

12 For arbitrary signal: On detector response y 0 (x) – spectrum before the detector y 1 (x 1,x) – detector response function y 2 (x) – spectrum, registered in detector x=E – current energy in spectrum x 1 – the energy of photon line Forming of signal: For photon line: Spectrum in detector will be: In the assumption that x j > x i by j > i

Reconstruction of the spectrum y 0 (x) using monochromatic lines on y 2 (x) Function of the response y 1 (x 1,x) 13

For continuous spectrum the function y 2 (x) is determined using only one point x = x k : 14

How to take into account the radiation of impurities We can write our system of equations: Signal from impurities: − the efficiency ε ij for k-th impurity 15 The activity of impurities for 51 Cr 3 MCi, obtained on results of the 1994 yr source experiment: 59 Fe 6∙10 9 Bk, 182 Ta 9∙10 9 Bk, 60 Co 2∙10 10 Bk, 46 Sc 3∙10 11 Bk − the activity of k-th impurity from the i-th part of the source Assuming the dependence of the activity of impurities on the source activity : The number of unknowns: N+K: {B i } + {p k } The signal in detector in presence of impurities:

Uncertainties of the method 1) Geometry of source and of detector (size, density of medium for absorption, relative location of the source and detector, direction of collimator,…) 2) Knowledge of spectrum of the source irradiation (accuracy of the available calibration of γ-sources > 3%, the IB spectrum is known only in the first approximation, …) 3) Accuracy of calculation of efficiencies and response functions 16 4)Statistics of events: The number of events on the «average» part of the spectrum: in case the efficiencies of the signal recorded from the «near» and «far» parts of the source differ on the order, then I.e. the minimal statistics N > 1100 for one Е interval And the summarized statistics > 27∙1100 = 3∙10 4.

Absolute measurements of statistics and spectrum of IB of 51 Cr We shell use 2 point sources of 51 Cr with activities: 1) ~ 20 mCi (10 9 Bq) and 2) ~ 1 kBk 17 Source №1 1)Measurement of the IB spectrum above 320 keV through collimator 2)The same measurements with collimator covered with Pb 2.6 cm: to control of the quality of measurements spectrum because of the pulses imposition Source №2 1)Measurement of the total counting rate in 4π-geometry with a couple of NaI detectors 2) Measurement of the rate of 320 keV line in Ge detector through collimator

Summary 1)Measurements of activity of intense source on measurement of continuous spectrum of γ-radiation 2) Reconstruction of spectra on measurements in SCD 3)Absolute calibration of the activity and of the measurement of the IB spectrum of the 51 Cr source 18 The following methods have been developed:

Thank you 19